Some Arithmetic Properties of Overpartition K -tuples
نویسندگان
چکیده
Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime and r is a quadratic nonresidue mod t.
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